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Polarizable Mean-Field Model of Water for Biological Simulations with Amber and Charmm force fields

Igor Leontyev, Alexei Stuchebrukhov

arXiv:1505.01454v1physics.chem-ph

TL;DR

Biological simulations often use older non-polarizable water models, while polarizable water models are incompatible with standard non-polarizable force fields. The paper presents an effective polarizable model that adjusts water dipoles to local environments while retaining that compatibility. It captures major water-property changes associated with local hydrogen-bond order and is proposed as a way to improve biological simulations without losing computational efficiency.

  • Problem

    Biological simulations largely use non-polarizable water models, while polarizable models are incompatible with standard non-polarizable force fields.

    Source: §1 · pp. 2–3

  • Method

    The model treats generic electronic screening implicitly and adjusts water's effective dipole to the mean field of its local environment.

    Source: §1 · p. 3, §4 · pp. 23–24

  • Results

    The model captures major water-property changes associated with varying local hydrogen-bond order and can naturally improve biological simulations without losing computational efficiency.

    Source: §4 · p. 25

  • Takeaways & Limitations

    The model behaves like TIP3P or SPC/E in bulk liquid while adjusting parameters inside proteins and at interfaces.

    Source: §4 · pp. 23–24

    The approach misses out-of-plane water polarization and protein polarization effects, and is not applicable to systems in vacuum.

    Source: The averaging technique and… · p. 15, Liquid water simulations · p. 20

Abstract

from arXiv · show

Although a great number of computational models of water are available today, the majority of current biological simulations are done with simple models, such as TIP3P and SPC, developed almost thirty years ago and only slightly modified since then. The reason is that the non-polarizable force fields that are mostly used to describe proteins and other biological molecules are incompatible with more sophisticated modern polarizable models of water. The issue is electronic polarizability: in liquid state, in protein, and in vacuum the water molecule is polarized differently, and therefore has different properties; thus the only way to describe all these different media with the same model is to use a polarizable water model. However, to be compatible with the force field of the rest of the system, e.g. a protein, the latter should be polarizable as well. Here we describe a novel model of water that is in effect polarizable, and yet compatible with the standard non-polarizable force fields such as AMBER, CHARMM, GROMOS, OPLS, etc. Thus the model resolves the outstanding problem of incompatibility.

1. Introduction

Water influences solvation, protein interiors, molecular motion, binding, and electrostatic interactions, yet biological simulations largely rely on older non-polarizable models. The paper introduces an effective polarizable water model designed to adapt to local environments while remaining compatible with standard non-polarizable force fields.

1. Introduction

  • Water solvates molecules, penetrates proteins, and affects molecular motion, binding, charge solvation, and electrostatic screening.The introduction identifies water as an integral part of enzymes as well as the surrounding solvent.Source: §1 · p. 2
  • Biological simulations mostly use older models such as TIP3P and SPC, which are non-polarizable and do not reflect water's differing properties across environments.The cited models were developed almost thirty years ago and only slightly modified since then.Source: §1 · p. 2
  • Polarizable water models address environmental polarization differences, but conflict with standard non-polarizable force fields because their parameterization strategies differ.The paper identifies AMBER, CHARMM, GROMOS, and OPLS as examples of standard force fields.Source: §1 · p. 2
  • The proposed model separates generic condensed-medium electronic screening from local protein-charge effects, enabling compatibility with standard non-polarizable force fields.It adjusts water dipoles to the local environment while retaining computational efficiency similar to TIP3P-like models.Source: §1 · p. 3

2.1 Electronic screening, MDEC model

Water needs different charge distributions in different environments, while similar configurations such as bulk liquid can be represented by averaged molecular parameters. The MDEC framework treats electronic screening implicitly and separates it from polarization due to local charges.

2.1 Electronic screening, MDEC model

  • Different environments require different water charge distributions because isolated and liquid water have different dipole moments.The passage gives a vacuum dipole of 1.85 D and a liquid value of about 3 D.Source: §2.1 · p. 4
  • For similar configurations, fixed molecular parameters can represent the average charge distribution, with remaining fluctuations included through renormalization or scaling.The passage describes bulk liquid water as an example of a configuration class with a well-defined average.Source: §2.1 · p. 4
  • MDEC represents electronic screening through an electronic continuum while using effective scaled charges rather than explicitly modeling electronic polarizability.The continuum must be included in certain calculations, including free energies, dielectric properties, and vaporization energies.Source: §2.1 · p. 5
  • The framework separates continuum-induced repolarization from additional repolarization caused by local charges, allowing response to environment-specific charge distributions.The passage identifies hydrogen-bonded neighbors as an example of local charges that repolarize water.Source: §2.1 · pp. 5–6

2.2 MDEC Hamiltonian

The MDEC Hamiltonian combines molecular repolarization and solvation terms with screened intermolecular electrostatics. It relates this treatment to standard force fields while identifying mismatches for ionic groups and the need for water parameters that adapt to local solvation conditions.

2.2 MDEC Hamiltonian

  • The Hamiltonian is constructed by repolarizing molecules from gas-phase to condensed-phase states, transferring them into the electronic continuum, then adding screened intermolecular interactions.The self-energy and solvation-energy terms are constants for fixed-charge models and do not explicitly contribute to intermolecular forces, though they matter for energy calculations.Source: §2.2 · pp. 6–7, In these notations the electrostatic… · p. 8

In these notations the electrostatic part of the MDEC model Hamiltonian is written as

  • The MDEC Hamiltonian includes repolarization self-energy, electronic solvation energy, and screened intermolecular interactions.Its screened interaction term depends on the electronic dielectric screening factor and the types of molecules in the interacting pair.Source: §2.2 · pp. 6–7
  • For point-charge models, electronic screening scales effective charges and dipoles by a common factor, preserving system charge neutrality.The passage describes this scaling for screened interactions in the MDEC point-charge treatment.Source: §2.2 · p. 8

Relation to Standard force fields models

  • MDEC electrostatic interactions match conventional non-polarizable force fields for neutral groups, but standard force fields treat ionic groups with unscreened integer charges.The paper says ionic charges should be additionally scaled for consistency with electronic screening.Source: Relation to Standard force fields models · pp. 8–9
  • Standard integer ionic charges disregard electronic screening, leading to overestimated direct charge interactions and ion-solvent interactions.The paper describes these mismatches relative to the electronic screening inherent in the condensed medium.Source: Relation to Standard force fields models · p. 9

Water models

  • Liquid-water dipoles are reported as 2.7–3.2 D, whereas TIP3P uses a 2.35 D effective dipole understood as a scaled value.The liquid dipole estimate is debated, and the passage notes its dependence on the partitioning scheme.Source: Water models · pp. 9–10
  • Water parameters need adjustment across solvation conditions because low-dielectric protein or membrane environments differ from the liquid-water reference environment.The passages identify water dipole dependence on environment and note that biological applications include variable solvation conditions.Source: Water models · pp. 10–11

2.3 Mean Field Polarizable Model of Water

The model represents water polarization through an effective dipole that responds to the local electric field, while treating generic electronic screening consistently with non-polarizable force fields. Its parameters target TIP3P properties for compatibility with biological force fields, and its temporal averaging and nonlinear response address self-consistency and strong fields.

2.3 Mean Field Polarizable Model of Water

  • The model relates an effective dipole to the effective field through an effective polarizability, with the equilibrium moment defined in an electronic continuum without surrounding charges.Different local charge environments then change the field acting on the molecule and adjust its effective parameters.Source: §2.3 · pp. 11–12
  • The parameters were selected to reproduce TIP3P properties because AMBER and CHARMM parameters were optimized for TIP3P, so a better solvent model does not guarantee compatible protein–solvent interactions.Source: §2.3 · p. 12
  • PCM calculations give an effective equilibrium dipole of 1.8 D; the spherical-cavity point-dipole estimate is close to 1.6 D but does not accurately substitute for TIP3P’s charge distribution.Source: §2.3 · pp. 12–13

The averaging technique and self-consistency

  • Temporal averaging damps each step’s field-driven dipole adjustment, smoothing stochastic field fluctuations and allowing the water molecules’ moments to reach self-consistency.The relaxation time sets how quickly the model responds to changes in the polar environment.Source: The averaging technique and… · pp. 14–15
  • Adjusting partial charges is computationally efficient and needs no additional interacting sites, but fluctuating-charge models cannot handle out-of-plane water polarization.For 2,048 water molecules, benchmark performance was within 10% of original TIP3P.Source: The averaging technique and… · p. 15

Non-linear polarization

  • The model makes effective polarizability depend on electric-field strength to prevent polarization catastrophe, with the critical field E* adjustable.Source: Non-linear polarization · p. 16

3. Simulation details and Results

MFP/TIP3P preserves TIP3P behavior in bulk while adapting water polarization to local protein environments. Its averaging timescale and condensed-phase assumptions shape where the model is applicable.

Simulation protocol

  • The model uses dynamically changing TIP3P charges and an adjustable nonlinear cutoff fitted to reproduce TIP3P bulk density; simulations used 298 K and 1 atm.Protein simulations used Amber, and each property was sampled over 4 to 8 simulations with 0.5 ns equilibration followed by 10 ns data collection.Source: §3 · p. 16, Simulation protocol · pp. 17–18

3. Simulation details and Results

  • A 5 ps averaging time balances accuracy and temporal resolution; the authors expect it to be less critical in uniform bulk or slowed protein environments than at interfaces.The model is described as performing better than TIP3P when the environment changes substantially within the diffusion distance.Source: §3 · pp. 16–17

Liquid water simulations

  • MFP/TIP3P reproduces TIP3P liquid properties at ambient conditions, including identical gOO, gOH, and gHH radial distribution functions.The stated target is agreement with TIP3P in bulk, not correction of TIP3P's own imperfections relative to experiment.Source: Liquid water simulations · pp. 18, 20
  • From arbitrary initial dipoles, bulk water relaxes to self-consistent parameters matching TIP3P, and including Eself and ΔGel is essential to match its energy.For a small cluster, relaxation is expected to be close to τ=5 ps.Source: Liquid water simulations · pp. 18–19

Protein simulations

  • Water polarization averages lower inside the protein than outside, with Mg2+-ligated waters near 2.8D and hydrophobic-cavity waters down to 1.8D.The passages associate weaker hydrogen bonding in hydrophobic cavities with depolarization.Source: Protein simulations · pp. 21–22
  • At essentially the same computational cost, MFP/TIP3P captures local protein-environment changes in water polarization that fixed-charge TIP3P cannot represent.The model is reported to improve simulations in non-uniform biological environments without essentially losing computational efficiency.Source: Protein simulations · pp. 21–23

4. Conclusions

The conclusions present MFP as a mean-field polarizable water model designed to work with existing non-polarizable biological force fields. It reproduces TIP3P bulk behavior and responds to local environments, with stated boundaries on its scope and polarization effects.

4. Conclusions

  • The model separates generic condensed-phase electronic screening, represented by scaled charges, from water-charge adjustment to the local polar environment.It adjusts effective dipoles to the mean field rather than the instantaneous field, matching the approach of non-polarizable effective force fields.Source: §4 · p. 23
  • The approach assumes a condensed-phase electronic continuum and omits out-of-plane water polarization and protein polarization effects.It is not suitable for small water clusters in vacuum.Source: §4 · pp. 24–25
  • MFP/TIP3P is optimized to reproduce TIP3P bulk properties, allowing replacement of TIP3P in typical solvation conditions without inconsistency with AMBER or CHARMM.The optimization target is TIP3P rather than actual liquid-water properties.Source: §4 · pp. 24–25
  • In protein environments, MFP/TIP3P captures local water-property changes, and the authors say it can improve biological simulations without losing computational efficiency.The conclusion attributes major water-property changes to variation in local hydrogen-bond order.Source: §4 · p. 25

Associated Content

The supporting information lists a derivation of the MDEC effective Hamiltonian and analysis of how MFP/TIP3P properties depend on mean-field time resolution.

Associated Content

  • Supporting information covers the MDEC effective-Hamiltonian derivation and the dependence of MFP/TIP3P water properties on mean-field time resolution.Source: Associated Content · p. 25

Figure Legends

The figure legends cover MDEC bulk assembly, effective fields, water relaxation, ion solvation, and water dipoles around cytochrome c oxidase. They also describe the MFP and TIP3P radial distribution function curves as almost identical.

Figure Legends

  • Figure 1 partitions bulk MDEC assembly into gas-phase polarization and geometry change, electronic-continuum solvation, and addition of screened molecular interactions.Source: Figure Legends · p. 32
  • Figure 2 compares local-basis effective-field distributions: TIP3P components are marked by triangles, circles, and squares, while MFP/TIP3P uses solid lines.Source: Figure Legends · p. 32
  • Figure 3 shows relaxation of 2,048 MFP/TIP3P waters from near-zero partial charges and compares TIP3P ensemble fluctuations at 298 K.The plotted quantities include average dipole moment, local-basis field, and potential energy per molecule.Source: Figure Legends · p. 32
  • Figure 4 compares ion-solvating water dipoles, instantaneous fields, and oxygen–ion radial distributions for scaled and unscaled ion charges.Scaled-charge TIP3P solvent distributions are included for comparison.Source: Figure Legends · p. 32
  • Figure 5 shows water dipole distributions around cytochrome c oxidase, grouped by CuB distance and water ligation or cavity location.Its black curve averages over spherical slices and is shown only where the averaging is statistically meaningful.Source: The MFP (red) and TIP3P (black dashed)… · p. 33
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